Signal modulation has historically been impressed on an intermediate frequency (IF) or radio frequency (RF) carrier by using a rectangular coordinate system. The rectangular coordinates are normally referred to as the in-phase (I) and quadrature-phase (Q) components. The I-channel is used to directly modulate a cosine-carrier signal and the Q-channel is used to directly modulate a sine-carrier signal. The modulated carriers are then summed and amplified to form the desired transmit signal. This approach is very general and can in principle be used to create any transmit waveform of interest. It is hereinafter referred to as IQ modulation in this disclosure.
Polar modulation is an alternative modulation method which is mathematically identical to IQ modulation. Polar modulation is capable of exhibiting much better power amplifier efficiency than IQ modulation and is of great interest in the low-power communications industry for that reason.
Modern communication systems make substantial use of digital signal processing methods. The I- and Q-channel modulation signals are normally represented by a series of synchronous discrete time samples that can be represented by the sample pairs (Ik, Qk). The equivalent polar representation of this same signal is given by Rk∠θk, in which Rk is the magnitude of the signal modulation and θk is the phase of the modulation. Mathematically, the IQ modulation and polar modulation coordinate samples are related by:Rk=√{square root over (Ik2+Qk2)}θk=tan−1(Qk,Ik)  (1)andIk=Rk cos(θk)Qk=Rk sin(θk)  (2)
One of the most severe problems associated with polar modulation is that the signal bandwidth of the polar modulation is normally much larger than the bandwidth of the IQ modulation system. This is especially true for the phase component. Although the mathematical relationships given by (1) and (2) are exact, they are also highly nonlinear, leading to severe bandwidth expansion in application. A bandwidth-limited IQ modulation signal does not in general create a bandwidth-limited polar signal.
One of the major causes of this problem is modulation signal trajectories that pass near the origin of the signal constellation. Such signal trajectories can produce severe spiking behavior in the phase channel, resulting in severe bandwidth expansion. In order for systems to effectively employ polar modulation and exploit its benefits in the power amplifier area, bandwidth reduction of the polar modulation waveforms is very desirable if it can be accomplished without causing other serious impairments to system performance.